Let the initial deposit be sum of the present value of the two later withdrawals

PV= 5000*PVIF(8%,3)+7000*PVIV(8%,6)

3969.16120510085 =5000/(1+0.08)^3
4411.18738818173 =7000/(1+0.08)^6
Total 8380.34859328258 =SUM(B8:B9)

The amount of ₹ 8380 grows to a value of ₹ 10,559 in three years; ₹5000 is withdrawn then,leaving ₹ 5559.This a
today will result in the desired withdrawals.

₹ -3,969.16
₹ -4,411.19
₹ -8,380.35

FV of rs 8380,35 after 3 years ₹ 10,556.83

Withdrawal 5000
Balance ₹ 5,556.83

FV ₹ -7,000.00
 7002.739

en,leaving ₹ 5559.This amount is left for another three years to compound to the desired of ₹7000.Therefore an amount of ₹ 8380 depo

₹ -251.94 ₹ -251.94
e an amount of ₹ 8380 deposited
The firm borrows ₹ 17,00,000 (85%). Compound interest occurs over the entire 11 years of the life of the loan.In o
( 1) the loan repayment will be computed by using a PVIFA table
(2) The present value of an annuity located one year before the first payment.

To compute the size of the annual payment,first compute the amount owned at the end of year 3 ( one year befo
FV 2201549 =1700000*(1+0.09)^3
Now ,the FV becomes the PV of the 8- payment annuity discounted at 9%. So, compute the equal yearly payment
2201549=X* PVIFA(9%,8)
Annuity amount ₹ 397,763.50
The plant expansion financing plan can be summarized as follows:
Down payment at year zero of ₹ 300000;the balance borrowed at 9% interest.Eight yearly loan repayments of ₹
ears of the life of the loan.In order to obtain the req. annual loan payment; two additional points have to be remembered

end of year 3 ( one year before the first payment).By compounding ₹ 17,00,000 for the three years at 9%

ute the equal yearly payment

yearly loan repayments of ₹ 397763.50 are to be made beginning at the end of the year 4
remembered
Assume that if the bond is purchased now, the first interest payment will be received in one year and that the bo
The yearly interest payment will be ₹ 80 ( 8% of ₹ 1000).In year 20 a payment of ₹1080 will be received ( ₹ 1000+

PV= Annuity payment*PVIFA(10%,20)

₹ 681.09

Now, the PV of the ₹1000 receivable at the end of year 20 can be found by discounting for 20 years at 10% intere

PV= 1000*PVIF(10%,20)
148.64363
The max. price is thus ₹ 681.09+148.6436= ₹830.12
in one year and that the bond will mature 20 years from now.
will be received ( ₹ 1000+800)

681.12

for 20 years at 10% interest

Obtain the compounded amount of the 10-payment savings annuity of ₹ 2000 corresponding to 10 payments an
FV= Annuity *FVIFA (7%,10)
₹ 27,632.90 =FV(7%,10,-2000)

The amount of ₹ 27632 is available immediately after the last payment.Now compund the amount of ₹ 27632 fo

FV=PV*FVIF(7%,5)
₹ 38,755.31

Finally, obtain the size of the equal retirement annuity payment by using the amount of ₹ 38,755.31 as the PV of
PV= annuity * FVIFA( 7%,20) PVIFA
₹ 3,658.23 =PMT(7%,20,-38755.31)
onding to 10 payments and 7%

the amount of ₹ 27632 for 5 year as single payment at 7%

₹ 38,755.31 as the PV of the retirement annuity.

2712.872 945.358

1937.766 2073.409
The minimum amount in this case is the PV of the series of amount due discounted at 14%

Year amount duPV

0 5000 5000
1 6000 5263.158
2 8000 6155.74
3 9000 6074.744
4 10000 5920.803
28414.44 The minimum acceptable amount
unt due discounted at 14%
 Loan Amortisation schedule
Annual Principal
installme Interest Repayme
Year Opening balance nt @ 15% nt Closing balance
Annual installmet 1 1000000 298312 150000 148312 851688
2 851688 298312 127753.2 170558.8 681129.2
3 681129.2 298312 102169.4 196142.6 484986.58
4 484986.58 298312 72747.99 225564 259422.567
5 259422.567 298312 38913.39 259422.6 0

Annual Installment=principle+interest
₹ -298,315.55
 Annuity@14%
0 22618.5
1
2
3
4
5
6
7 56603
8 10000
9 10000
10 10000
11 10000
12 10000
13 10000
14 10000
15 10000
16 10000
17 10000
18 10000
19 10000
Annuity@14%
56603*pfiv(14%.7) 56603*0.3996 ₹ 0.00

10000*PVIFA(14%,12) 10000*5.6603 ₹ 56,602.92

₹ 54,527.33

$56,602.92

$19,842.67
 20%

6000*FVIFA(X%,20)=44650
₹ 13,147.38

100000=X*PVIFA(10%,15y)
(a) 9375 9375
( b) 7500
₹ 495,588.68
495589.3

50445000
650000 1
2
10% 3
4
5
6
7
8
9
10
 ₹ 9,954.05 ₹ -9,954.05

₹ 23,471.13
₹ 23,471.13
3000
Purchase price 120000
DP -20000
Borrowing 100000
n 360
Interest rate 0.006667

Mortage payment ₹ 733.76

 To help solve this problem, we set up the information on a time line. As Figure 8 shows, Grant will save $

Solving this problem involves satisfying the following relationship: the present value of savings (outflows

Step-1 Find the future value of the savings of $2,000 per year and index it at t = 15. This value tells us how much

Amt -2000
r 8%
N 15
FV(t15) ₹ 54,304.23

Step-2 Find the present value of the retirement income at t = 15. This value tells us how much Grant needs to m

Amt 100000
rate 8%
N 20
Value at t40 ₹ 981,814.74
The present value amount is as of t = 40, so we must now discount it back as a lump sum to t = 15
Amt ₹ 981,814.74
rate 8%
N 25
Value at t15 ₹ 143,362.53

Step-3 Now compute the difference between the amount Grant has saved (Step 1) and the amount she needs t

Therefore, in present value terms, the annuity from t = 16 to t = 40 must equal the difference between th
₹ 89,058.30
Therefore, we must now find the annuity payment, A, from t = 16 to t = 40 that has a present value of $8
Amt ₹ 89,058.30
rate 8%
N 25 ₹ 371,901.16
annuity value ₹ 8,342.87
Grant will need to increase her savings to $8,342.87 per year from t = 16 to t = 40 to meet her retiremen

₹ 609,913.58 ₹ 981,814.74
e 8 shows, Grant will save $2,000 (an outflow) each year for Years 1 to 15. Starting in Year 41, Grant will start to draw retirement income o

value of savings (outflows) equals the present value of retirement income (inflows). We could bring all the dollar amounts to t = 40 or to

his value tells us how much Grant will have saved

₹ 371,901.16

₹ 8,342.87

ow much Grant needs to meet her retirement goals (as of t = 15). Two substeps are necessary. First, calculate the present value of the ann

16 ₹ 4,344.34

a lump sum to t = 15

nd the amount she needs to meet her retirement goals (Step 2). Her savings from t = 16 to t = 40 must have a present value equal to the d

l the difference between the amount already saved ($54,304.23) and the amount required for retirement ($143,362.53).

at has a present value of $89,058.30.

73.106
₹ 609,914.08

= 40 to meet her retirement goal of having a fund equal to $981,814.74 after making her last payment at t = 40.
rt to draw retirement income of $100,000 per year for 20 years. In the time line, the annual savings is recorded in parentheses ($2) to sho

dollar amounts to t = 40 or to t = 15 and solve for X

₹ 609,913.58

ate the present value of the annuity of $100,000 per year at t = 40. Use the formula for the present value of an annuity. (Note that the pre

24

e a present value equal to the difference between the future value of her savings and the present value of her retirement income

$143,362.53).
n parentheses ($2) to show that it is an outflow. The problem is to find the savings, recorded as X, from Year 16 to Year 40

nnuity. (Note that the present value is indexed at t = 40 because the first payment is at t = 41.) Next, discount the present value back to t =

tirement income
r 16 to Year 40

nt the present value back to t = 15 (a total of 25 periods).

12000=1800*PVIFA(x%,10)

6.666667 0.15

8% 12078.18
9% 11551.86

526.32
0.012667
0.066667 0.000127 0.080127
0.000127

0.462651
0.537349
6.706249
12071.25
 1200000

A 360000 Pay now B

840000 bal amt after 2 year 0 Py now
PV 720164.6 1 400000 0.925926 370370.37037
1080165 2 400000 0.857339 342935.52812
3 400000 0.793832 317532.89641
PV 1030838.795
prefer
C
Cash discount
1080000
Year
0
1
2 20000 23762 2000*FVIFA(9%,3)
3 20000 21800 0.295029
4 20000 65562 3.2781
5 65562
6 77894.21
 0
1X ₹ 2,881.73 FVIA ₹ 2,881.77
2X
3
4
5
6
17
18 20000 ₹ 74,464.96 PVIFA 20000
19 20000 19047.62
20 20000 18140.59
21 20000 17276.75
25.84
.\
#VALUE!
#VALUE!

74464.96
 0 Annual cost 7000 ₹ 2,221.58
1
2
3
4
17 ₹ 62,677.13
18 ₹ 16,846.33 0.943396 ₹ 15,892.77
19 ₹ 17,688.65 0.889996 ₹ 15,742.84
20 ₹ 18,573.08 0.839619 ₹ 15,594.32
21 ₹ 19,501.74 0.792094 ₹ 15,447.20
 pvifa 28.213
₹ 2,221.57

req future ₹ 16,846.33

₹ 17,688.65

7000

7350

16846.3346
17688.6514
1000*(1.12) x (1.06) x (1.08)
= $1,282
Cost of trip after 3 years- 142000*(1+0.06)^3= 169124.27

FV=PV*(1+r)^n
Money required to invest in mutual fund= 169124.27/(1+0.08)^3=134256.30
Invest in equity mutual fund for 8 year @ 15%p.a= 200000*(1+0.10)^8= 428717.76
If she Continued to invest in saving bank a/c= 200000*(1+0.04)^8 = 273713.81
Differ= 428717.76-273713.81=155004
The PQR ltd borrow= 850000
First compute the amount owned at the end of year 3
FV= PV*(1+r)^3= 850000*(1+0.08)^3=1070755
Now the FV becomes the PV of the 8-payment annuity discounted at 8%
PV= Annuity payment*PVIFA( 8%,8)
1070755=Annuity payment*5.747
Annuity payment=186316
Eight yearly loan repayment of ₹ 186316 are to be made beginning at the end of year 4
First two year interest rate @ 9%:- 67000*(1+0.09)^2 =79602.70
Next three years interest rate @8%:- 79602.70*(1+0.08)^3=100276.48
Next two years interest rate is 9%:- 100276.48*(1+0.09)^2=119138.48
Remaining phase of one year interest rate is @8%:- 119138.48*(1+0.08)=128669.56
FV = A * [(1+i)^n – 1] / i FV = 8000*[(1+0.08/4)^5*4 – 1] / (0.08/4) FV = ₹ 194379

Effective Rate of Interest = (1+0.08/4)^(4*1) – 1 = 8.24%

PVA = A* [{(1+r) n – 1} / [r *(1+r)n]
1200000/3.5172
Annual Instalment=₹ 341177

Year Opening Balance Annual Instalment Interest @ 13% Principal Instalment

1 1200000 341177 156000 185177
2 1014823 341177 131927 209251
3 805572 341177 104724 236453
4 569119 341177 73985 267192
5 301927 341177 39251 301927
Closing Balance
1014823
805572
569119
301927
0
8.189874 6.1051

7.44534 6.71561

31.04607
0
1
2
3
4
5